How to control the number of particles with a custom slider
Add an update function to your property which would be called whenever you change the that property :

def update_particles(self, context):
    bpy.data.particles['ParticleSettings'].count =bpy.context.scene.mycount_particles 

bpy.types.Scene.mycount_particles = bpy.props.IntProperty(
    name = "particle count", 
    default = 300, 
    min =0,
    max=10000, 
    update = update_particles,   
    description = "particles number of the first particle system"
    )